Chapter 2, Problem 56P

(a)

To determine

To identify: Whether the object is moving in positive or negative direction for segment A to B.

Answer to Problem 56P

The object is moving in the negative direction.

Explanation of Solution

Introduction:

Consider the given graph as shown below.

  

For the segment A to B, object is moving constantly and then distance decreases rapidly with time.

In the graph segment A-B, the object is moving in a negative direction as the slope of the line segment is decreasing over time.

Conclusion:

The object would be moving in the negative direction.

(b)

To determine

To identify: Whether the object is speeding up or slowing down in graph for segment A to B.

Answer to Problem 56P

The object is speeding up.

Explanation of Solution

Introduction:

Consider the given graph as shown below.

  

For the segment A to B, object is moving constantly and then distance decreases rapidly with time.

In the segment A to B, the object is moving from a less steep position to steeper one, this suggests that the object is speeding up.

Conclusion:

The object is speeding up.

(c)

To determine

To identify: Whether the acceleration of an object is positive or negative for segment A to B.

Answer to Problem 56P

The acceleration of the object is negative.

Explanation of Solution

Introduction:

Consider the given graph as shown below.

  

For the segment A to B, object is moving constantly and then distance decreases rapidly with time.

During the interval of A to B, the graph is going concave downward i.e. slope is going more negative. Thus, the acceleration is negative.

Conclusion:

The acceleration of the object is negative.

(d)

To determine

To identify: Whether the object is moving in positive or negative direction for segment D to E.

Answer to Problem 56P

The object would be moving in a positive direction.

Explanation of Solution

Introduction:

Consider the given graph as shown below.

  

For the segment A to B, object is moving constantly and then distance decreases rapidly with time.

For the segment D to E, object’s distance increases with time then the objects moves faster.

In the graph segment D-E, the object is moving in a positive direction as the slope of the line segment is increasing.

Conclusion:

The object would be moving in a positive direction.

(e)

To determine

To identify: Whether the object is speeding up or slowing down for segment D to E.

Answer to Problem 56P

The object is speeding up.

Explanation of Solution

Introduction:

Consider the given graph as shown below.

  

For the segment A to B, object is moving constantly and then distance decreases rapidly with time.

For the segment D to E, object’s distance increases with time then the objects moves faster.

The object is moving on the graph from a less steep position to steeper that is slope is increasing with time.This suggests that the object is speeding up.

Conclusion:

The object is speeding up.

(f)

To determine

To identify: Whether the acceleration of an object is positive or negative in the graph segment D to E.

Answer to Problem 56P

The object will accelerate.

Explanation of Solution

Introduction:

Consider the given graph as shown below.

  

For the segment A to B, object is moving constantly and then distance decreases rapidly with time.For the segment D to E, object’s distance increases with time then the objects moves faster.

During the interval D to E, the graph is going concave upward i.e. slope is going more positive. Thus, the acceleration is positive.

Conclusion:

The object will accelerate.

(g)

To determine

To identify: Whether the object moving in the positive or negative direction in the graph segment C to D.

Answer to Problem 56P

The object is not moving in either direction. The object is at rest.

Explanation of Solution

Introduction:

Consider the given graph as shown below.

  

For the segment A to B, object is moving constantly and then distance decreases rapidly with time.

For the segment C to D, the object’s distance is constant with time then object remains stationary.

After reading the graph segment C-D, the object is not moving in either direction. Thus, the distance graph is linearly constant.

Conclusion:

The distance between duration of graph segment C-D is constant. Thus, the object will remain at rest.

(h)

To determine

To identify: Whether the object speeding up or slowing down in graph segment C to D.

Answer to Problem 56P

The object is not moving in either direction. The object is at rest.

Explanation of Solution

Introduction:

Consider the given graph as shown below.

  

For the segment A to B, object is moving constantly and then distance decreases rapidly with time.

For the segment C to D, the object’s distance is constant with time then object remains stationary.

After reading the graph segment C-D, the object is not moving in either direction. Thus, the velocity of the object is zero.

Conclusion:

The velocity of the object is zero that is the object is at rest.

(i)

To determine

To identify: Whether the acceleration of the object positive or negative in the graph segment C to D.

Answer to Problem 56P

The object is not moving in either direction. So, the acceleration is zero.

Explanation of Solution

Introduction:

Consider the given graph as shown below.

  

For the segment A to B, object is moving constantly and then distance decreases rapidly with time.For the segment C to D, the object’s distance is constant with time then object remains stationary.

After reading the graph segment C-D, the object is not moving in either direction. Thus, the acceleration is zero.

Conclusion:

The object is not moving in either direction. So, the acceleration is zero.